Solving Schr\"odinger Equation with a Language Model

Abstract

Accurately solving the Schr\"odinger equation for intricate systems remains a prominent challenge in physical sciences. A paradigm-shifting approach to address this challenge involves the application of artificial intelligence techniques. In this study, we introduce a machine-learning model named QiankunNet, based on the transformer architecture employed in language models. By incorporating the attention mechanism, QiankunNet adeptly captures intricate quantum correlations, which enhances its expressive power. The autoregressive attribute of QiankunNet allows for the adoption of an exceedingly efficient sampling technique to estimate the total energy, facilitating the model training process. Additionally, performance of QiankunNet can be further improved via a pre-training process. This work not only demonstrates the power of artificial intelligence in quantum mechanics but also signifies a pivotal advancement in extending the boundary of systems which can be studied with a full-configuration-interaction accuracy.